Elliptic curve isogeny class 37632.3-k over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-37632.3-k
• Conductor: 37632.3
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 1 \); class number \(1\).

Elliptic curves in class 37632.3-k over \(\Q(\sqrt{-3}) \)

Isogeny class 37632.3-k contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
37632.3-k1	\( \bigl[0\) , \( -a\) , \( 0\) , \( -13 a + 70\) , \( 205 a - 63\bigr] \)
37632.3-k2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -68 a + 60\) , \( 40 a - 240\bigr] \)
37632.3-k3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -78 a + 125\) , \( -3161 a + 3294\bigr] \)
37632.3-k4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -3 a + 5\) , \( 4 a - 6\bigr] \)
37632.3-k5	\( \bigl[0\) , \( -a\) , \( 0\) , \( 22 a - 35\) , \( 51 a - 42\bigr] \)
37632.3-k6	\( \bigl[0\) , \( -a\) , \( 0\) , \( 122 a - 195\) , \( -769 a + 878\bigr] \)
37632.3-k7	\( \bigl[0\) , \( -a\) , \( 0\) , \( 322 a - 515\) , \( 3639 a - 3666\bigr] \)
37632.3-k8	\( \bigl[0\) , \( -a\) , \( 0\) , \( 1922 a - 3075\) , \( -51817 a + 55742\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 16 & 2 & 4 & 8 & 8 & 16 \\ 4 & 1 & 16 & 2 & 4 & 8 & 8 & 16 \\ 16 & 16 & 1 & 8 & 4 & 2 & 8 & 4 \\ 2 & 2 & 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 4 & 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 8 & 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 8 & 8 & 4 & 2 & 4 & 1 & 8 \\ 16 & 16 & 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph